= Solution
Stop <rejection sampling> when exactly $N=66{,}564$ target draws have been accepted. The total proposal count $T_N$ is a sum of $N$ <independent> waiting times with <geometric distribution>, equivalently a <negative binomial distribution> counting trials. Consequently
$$
\boxed{\mathbb ET_N=MN=66{,}564M,\qquad\operatorname{Var}(T_N)=NM(M-1).}
$$
The accepted-sample <Monte Carlo estimator> then has the approximate $99\%$ precision from (a)(iii). The displayed proposal cost is an <expected value>, which need not be an integer. Spending this many proposals in advance does not ensure that $N$ target draws will have been accepted.
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